Animating eye texture in a head mesh
You can use an addon called Animall to animate the texture.


CYCLES


Activate an AnimAll add-on (File--> User Preferences--> Addons--> AnimAll). It'll be displayed in the tools menu in the 'Animation' section.





Setup the image texture in the Node Editor. Enter the "Edit Mode"and unwrap the mesh (press U in 3d window) using the Project from view.





In UV/Image Editor place the UV island on the desired part of the image texture (note that you have to make perfect spaces between images in graphics program. In this case the images have 200 px of space between them).





Check the 'UVs' box and insert the first keyframe (clicking 'Insert').





Go to the next frame (right arrow), place the UV island on the next part of the image texture (in this case i go 200 units along x axis) and inesert the keyframe again. Repeat this process moving right.





Place the UV island in the lower row (in this case I move the uv island -600 units along x axis and -200 units along y axis)





Continue the proces and position the UV island on the last image part (of course the moving patern could be different). Go to the 'Object Mode' and play the animation (alt+A).




8.- Select all keyframes on the dopesheet (or Graph editor) and set them to Constant 




You can also prepare the texture like this, so it will be easier to jump between images. Remember about doing perfect spacing between them.





Go to NLA Editor, change the action name (CTRL+LMB) and click the 'double arrow' icon.





Now you have your 'blink animation' in one block and you can place it wherever you like on the timeline.




Hope I helped.

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BLENDER INTERNAL RENDER

I'm adding an update, since Warianos wants to know how to do the same thing in Blender Internal. So here it goes:


Select the mesh you want to have an animated texture on it, and in Shading panel change the Material Mode from Multitexture to GLSL. Add a lamp (a sun lamp for example), so you'll be able to see the texture when you apply it.





With the object selected in Object Mode go to the Materials Panel. Add the material. Set the Diffuse and Specular values if you want.





Go to the Textures Panel, set the texture type to Image or Movie, then click the Open button in Image panel and load your image.





In Mapping panel set the Coordinates to UV. 





In 3d window set the Viewport Shading to Texture





Load an image in Uv/Image Editor window. Unwrap the mesh using Project from View option. Enable an AnimAll addon and check the Uvs box.





Now the process looks like in my previous answer. You press Insert in AnimAll panel and add a keyframe. Then you go to other frame, change the Uv island's position and press Insert again.






Being in Object Mode, with the Viewport Shading set to Texture you can now play an animation to check out how it looks like. If you don't want the smooth transition between images you may set the Curve Interpolation type to Constant, by pressing T in graph editor window (as Cegaton suggested in his answer).




Hope it is what you wanted to know.